How to solve Microwave Engineering Pozar chapter 05 exercise 25 with MATLAB

Question:



Literature source [POZAR] available here:
https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

There's also a solutions manual available here:
https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual


Answer:

MATLAB script source pozar_05_exercise_25.m and all necessary support functions included in .zip here attached file pozar_05_exercise_25.zip
including detailed explanation. Following, the key points:



for a load located here



the following 2-element L-shape match circuits are possible:



the values of the components are

C1 = 1.258213410121157e-12
L1 = 5.012370792994983e-09

L2 = 2.169965544798663e-08
C2 = 1.263388970843133e-12

the resulting fractional bandwidths are

df_ov_BW1 = 0.188090595470227
df_ov_BW2 = 0.194140292985351

there are 2 related errors in the solutions manual:

1.

this dw is f2-f1 so the calculation goes right to left, dw is a known parameter that along with the other values is used to verify

true(dw1*log(1/gamma_m)=<pi*R/L)
=
logical
1

true(dw2*log(1/gamma_m)=<pi*R/L)
=
logical
1

f2 and f1 are also obtained, dw1 dw2 being

dw1=2*pi*(f2_sol1-f1_sol1)

dw1 = 2.363105994030242e+09

dw2=2*pi*(f2_sol2-f1_sol2)

dw2 = 2.439132536247116e+09



2.


again, this 174% is not the fractional bandwidth of the only circuit suggested in the solutions manual, the fractional bandwidths for solutions are shown above.

John BG
jgb2012@sky.com